Transcript L07_Arcs

Upcoming Deadlines
Fifth Homework (Video analysis of Path of Action):
Due Friday, September 25th (This Friday);
15 points (10 points if late)
Sixth Homework (Outline of First Term Paper)
Due Wednesday, September 30th
Campus-wide Furlough Day
Monday, October 19th
(Art/Phys 123 will meet on Wed., Oct. 21st)
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Homework Assignment #5
Shoot reference of yourself doing a running jump.
Use the Tracker software to mark your path of
action while in the air (tracking center of torso).
Upload image showing track and graphs for one of
your jumps to your blog.
Record a clip showing the tracked motion.
Upload both original reference and the tracked
Quicktime clip to your blog.
For details, see course website; for an example, see
the course blog.
This assignment is due by 8am on Friday, September
18th (This Friday). 15 points
Homework Assignment #6
Write a one-page outline for your first
term paper.
The general topic for your first term paper is:
The Laws of Physics in an Animation Universe
Modern science is based on the principles of
experimental observation and theoretical analysis;
in this assignment you will apply these principles in
a critical analysis of animation and special effects.
Homework Assignment #6
For the term paper, you will select an animation film
(or a live-action film featuring CGI animation
special effects).
You will then formulate three distinct scientific
hypothesis for the universe portrayed in that film
(which may or may not obey the same physical laws
as the real world).
For example, in your animation’s universe the laws
gravity may be different (e.g., heavy objects may
fall faster than light objects).
Homework Assignment #6
Your hypotheses should be such that there is
relevant observational evidence in the film; you
need to describe what that evidence is and how it
supports your theories.
You will also formulate competing theories and
present evidence that the universe portrayed in
your film does not follow those alternate
hypotheses.
Homework Assignment #6
For this homework assignment you are to choose the
film that you'll analyze and write a one-page outline
for the term paper.
Post this outline on your blog; an example has been
posted on the course blog.
This assignment is due by 8am on Wednesday,
September 30th. (10 points; 5 points if late)
Note: The term paper will be due in mid-October.
Arcs in Animation
Disney’s Principles of Animation
In their classic book, Disney
Animation – The Illusion of Life, Frank
Thomas and Olie Johnston list a set of
basic principles for animation.
1.
2.
3.
4.
5.
Squash & Stretch
Timing
Anticipation
Staging
Follow Through
& Overlapping Action
6. Straight Ahead &
Pose-to-Pose Action
7. Slow In and Slow Out
8. Arcs
9. Exaggeration
10. Secondary Action
11. Appeal
Disney’s Principles of Animation
In their classic book, Disney
Animation
The Illusion
of discussed
Life, Frank
We– have
already
Thomasseveral
and Olieof
Johnston
list a set of
these principles
basic principles
for animation.
of animation,
specifically:
1.
2.
3.
4.
5.
Squash & Stretch
Timing
Anticipation
Staging
Follow Through
& Overlapping Action
6. Straight Ahead &
Pose-to-Pose Action
7. Slow In and Slow Out
8. Arcs
9. Exaggeration
10. Secondary Action
11. Appeal
Disney’s Principles of Animation
In their classic book, Disney
Animation
– The
Illusion
of Life,arcs
Frank
Today
we
will discuss
Thomasand
and how
Olie they
Johnston
list to
a set of
relate
basic principles
formotion.
animation.
animated
1.
2.
3.
4.
5.
Squash & Stretch
Timing
Anticipation
Staging
Follow Through
& Overlapping Action
6. Straight Ahead &
Pose-to-Pose Action
7. Slow In and Slow Out
8. Arcs
9. Exaggeration
10. Secondary Action
11. Appeal
Arcs of Motion
Motion usually follows an
arc, which may be simple,
like a circle. or very
complex and irregular.
Importance of Arcs
Disney animation legends Frank
Thomas and Olie Johnston write:
One of the major problems
for the inbetweeners is
that it is much more
difficult to make a
drawing on an arc.
Drawings made as straight
inbetweens completely kill
the essence of the action.
Circular Arcs
Circular arcs are common since
motion is often around a fixed
pivot point, such as a joint.
Speed in Circular Motion
Rotational Speed: Revolutions per second
Tangential Speed: Total distance per second
Same Rotational Speed
Different Tangential Speeds
Throwing Arm
The longer the
throwing arm,
the greater the
tangential speed
so the farther it
can throw.
Sling lengthens
the arm at almost
no cost in the
weight.
Doubling the arm length
quadruples the range!
Timing on Circular Arcs
A circular arc is a simple path of action but
the timing may be complex and textured.
In this golf swing the
motion:
• Slows out (accelerates)
to hit the ball
• Uniform after the hit
• Slows in as the swing
finishes follow-through
Rolling & Slipping
1
2
3
4
5
6
7
ROLLING
Rolling ball turns one revolution when it
travels a distance equal to three times
its diameter (actually 3.1416 diameter)
1
2
3
4
5
SLIPPING
Slipping and rolling are both uniform in spacing and rotation.
Wagon Wheel Illusion
In this illusion, the wheel seems to spin backwards.
Often seen
in westerns
Nyquist Effect
In this illusion is due to persistence of vision.
Illusion
Wheel on
frames
#1 and #2
#2
Actual
Rotation
#1
The brain tracks the movement of the spokes by
looking for the nearest location on each frame.
This effect limits how fast a wheel can spin in an
animation and still be seen as turning.
Uniform Rotation in Perspective
The timing for uniform rotation has
texture when seen in perspective.
Half orbit
Quarter
orbit
Rotation from key #1 to #5 in background takes
twice as long as from #6 to #8 in foreground.
Non-Uniform Circular Motion
Two common types of motion on circular arcs that
have non-uniform timing and spacing are:
Exponential Spacing
Example:
Tipping over
Pendulum Spacing
Example:
Stride in
walking
Tipping Over
Tipping over is a common example of motion
on a circular arc. Two ways to tip over:
X
Center tipped past
point of contact
Center past an edge
Tipping Rotation
A brick rotates about a point as it tips;
that point is the center of a circular arc.
X
Friction tends to keep the brick from sliding
until it loses contact with the table.
Exponential Spacing
Release
1
1
Constant acceleration (Odd Rule)
3
2
5
3
1
Release
7
4
2
3
Exponential Spacing
4
As the slope of the incline increases,
the acceleration itself accelerates.
Rolling off a Tipping Point
1 2 3 4
5
6
7
Peak
8
Slowing out from a tipping point is very slow
initially, but then accelerates rapidly.
Anticipation & Exponential Spacing
Play
Texture of the
timing as the brick
tips over creates
anticipation, which
you want at the
start of a scene
Also notice motion
blur near top of
brick, which has
large tangential
speed.
Pendulum Spacing
A pendulum’s path of action is also a circular arc
but the spacing is very different from the
exponential spacing of tipping over.
Spacing & Timing in Swinging
A pendulum will slow in and out as it
swings back and forth, the same as a
ball rolling in a half-pipe.
Play
Most of the texture in the timing is at the
endpoints; the timing is even in the center.
Motion Graph
#7
#1
Angle
The motion graph (angle vs. frame)
confirms that the timing is mostly
textured at the apexes.
#4
Frame
Swinging in Perspective
Visually the timing
has even more
texture when the
swing occurs in
perspective.
Who Framed Roger Rabbit? (1988)
The opening sequence in
Who Framed Roger
Rabbit? makes great use
of the textured timing
of arcs in perspective.
Animation by
Richard Williams
Demo: Don’t Flinch
Pendulum swings back and forth yet it
doesn’t hit your face.
Bowling Ball Pendulum
Play
This clip lets you
experience what it’s
like to do this demo.
Spirals
A spiral is just a circular arc with a radius
that’s either increasing (spiral out) or
decreasing (spiral in).
Concept art from
Pirates of the Caribbean 3
Rotational Speed in Spirals
If the radius decreases without pulling
the object inward then the rotational
speed increases (due to shrinking radius)
but the tangential speed stays constant.
Spacings along
the curve stay
constant.
Spiral In
Demo: Interrupted Pendulum
An “interrupt” bar changes the
radius of the arc for a pendulum.
Tangential speed
does not increase
due to the pendulum
whipping around the
interrupt bar.
Energy is not
increased by the
interrupt bar so ball
swings back to the
same spot.
Bar
Rotation in Spirals (cont.)
If the radius decreases by pulling the
object inward then the rotational speed
increases due to shrinking radius and due
to an increase in the tangential speed.
Spacings along
the curve get
bigger and
bigger.
Spiral In
Demo: Skater’s Spin
Slow
Rotation
FAST
Rotation
Exert a force to pull hand weights toward my body,
causing a big increase in rotational and tangential speeds
Rotation in Spirals (cont.)
If the tangential speed decreases (say by
friction) but inward force constant then
the rotational speed still increases.
Spacings along
the curve get
shorter
yet it
still
spins
faster
and faster.
Spiral In
Coin Vortex
How Does the Brick Fall?
Does the brick
rotate and then fall
down the side of
the table?
1
2
3
No! The brick does
4
not fall this way.
X
Play
Forces on the Tipping Brick
The table pushes on
the brick upward and
towards the right.
Gravity pulls downward
Center of the brick shifts
down and towards the right.
If no table…
Pushing Off by the Table
The table pushes away
on the brick, which
causes the brick to
move away from the
table as it falls.
Once it loses contact
with the table, only
the force of gravity
accelerates the brick.
Centrifugal Force
Insect inside a can rotating in a circle
When we move on an
arc, it seems to us
as if there is an
outward force,
pushing us away
from the center of
the circle.
Physicists call this
apparent force the
centrifugal force.
What we see
What the
insect feels
Class Demo: Bucket Overhead
I will put a bucket full of
water over my head without
getting wet. How?
By rotating it fast enough.
The water stays in the bucked
as if pressed into it by a
centrifugal force.
You experience
centrifugal force on
taking a sharp turn
Centrifugal
Force
Wile E. Coyote & Loop-D-Loop
Play
In reality, it is impossible
to travel upside-down, as
Wile E. Coyote does in this
scene. True or False?
“Beep Beep” (1952)
Demo: Loop-the-Loop
If the speed of
the ball is large
then not only
does it stay on
the track, the
ball even pushes
outward and
against the rail.
Release
Velocity
Demo: Loop-the-Loop
Ball could even
circle a loop
with a gap, if
the speed was
just right so
gravity was
equal to the
centrifugal
force.
Release
Velocity
GAP
Simulated Gravity
Centrifugal force could be
used to simulate gravity in
a space station.
With the right rate of
rotation a person on the
outer rim would feel as if
they stood on the surface
of Earth.
Scientifically accurate in
the movie 2001: A Space
Odyssey (1968)
Rotation
Simple Spinning
A falling brick may
turn byArbitrary
simple
spinning around its
center.
1
1
2
In simple spinning, the angle
rotates at a constant rate.
A brick tipped 45º as it loses contact
with the table will fall spinning about
30º every two frames.
3
3
5
4
7
Tumbling
A falling brick may
turn byArbitrary
a more
complicated
tumbling motion.
1
1
2
There is no simple way to
describe tumbling. However, the
brick’s center still follows the
same path of action.
3
3
5
4
7
Tennis Racket Theorem
SPIN
When an object
turns about its
middle axis, it
tends to tumble.
SPIN
TUMBLE
When an object
turns about its
long or its short
axis, it tends to
spin.
Irregular Objects
SPIN
TUMBLE
SPIN
SPIN
Spin or Tumble?
Rotation around two of
these axes is spinning.
The axis of rotation
that tumbles is:
A) Head-to-toe axis
B) Side-to-side axis
C) Front-to-back axis
A
B
C
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Creating Action
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